It was a dream for the first 20 or so days. One time, I was drain testing the battery, and the computer shut itself off due to a dead battery (I mistakenly thought Vista would automatically put it to sleep or something...). I plugged it in and everything was good to go.

Later that night or the next day, my computer crashed, I did not find the reason but the following day when I tried to turn it back on, I had to go through the "repair your computer" option, and everything seemed fixed.. Later, I got a Lexmark X7675 printer, and after installing the software, my computer refused to work. It booted once, but hung within a minute of logging in, and after that, I received a system_service_exception 0x0000003B error for all options: repair, normal boot, last working configuration, safe boot
Finally I had to use my recovery disk to get it working, and upon installing the software again, I thought it was causing problems, so I entered safe mode and removed it.
Two days later and I'm still having problems with hanging, except now I can hear my harddrive behaving strangely. When I was using AVG to scan my computer, it hung, and I had to restart. Using CHKDSK it repaired some files, including an avg log, but it froze at stage 5 at 63%. I forced shutdown and tried again, and it froze at the same empty sector.
I'm logged on again and everything seems to work, but occasionally my drive would make these repetitive clicking noises, and then go silent, and my harddrive usage light will just light periodically. The computer is hung at that point, and I can still move my mouse, but that's it.
I can't go to repair your computer option when booting up because I get the system_service_exception.
Speedfan's SMART analysis says my drive is healthy, and so does Vista's Computer Management, but I'm at a loss as to what to do - how can I tell if its a hardware failure for sure?
Also, I haven't been able to get iTunes to detect my iPhone after I used Gateway Recovery, not sure if that has any correlation...

Bad drives are not "unheard of".
I once bought a laptop where the hard-drive crashed in a matter of two weeks...
the seller just replaced my computer with a new one.

Sounds like you are still under warranty. I would suggest that as your first option.
Back up your data files, if you can...
Something like Apricorn's utility -might- help you, even if you cannot recover data through other means.